home prime of a number, follow this procedure: first, find its prime factors; then concatenate these by writing the prime factors in size order to form a new number using all of their digits; then repeat until the resulting number is prime.
For example, 9 = 3 × 3, so its prime factors are 3 and 3. These concatenate to give 33. Now, find the prime factors of 33. They are 3 and 11, which concatenate to give 311. Since 311 is prime, we stop and say that the home prime of 9 is 311.
The home prime of a prime number is the number itself. So, for example, the home prime of 2 is 2.